Quantifying chaperone-mediated transitions in the proteostasis network of E. coli.

Department of Chemistry, The University of Michigan, Ann Arbor, Michigan, United States of America.

Abstract

For cells to function, the concentrations of all proteins in the cell must be maintained at the proper levels (proteostasis). This task--complicated by cellular stresses, protein misfolding, aggregation, and degradation--is performed by a collection of chaperones that alter the configurational landscape of a given client protein through the formation of protein-chaperone complexes. The set of all such complexes and the transitions between them form the proteostasis network. Recently, a computational model was introduced (FoldEco) that synthesizes experimental data into a system-wide description of the proteostasis network of E. coli. This model describes the concentrations over time of all the species in the system, which include different conformations of the client protein, as well as protein-chaperone complexes. We apply to this model a recently developed analysis tool to calculate mediation probabilities in complex networks. This allows us to determine the probability that a given chaperone system is used to mediate transitions between client protein conformations, such as folding, or the correction of misfolded conformations. We determine how these probabilities change both across different proteins, as well as with system parameters, such as the synthesis rate, and in each case reveal in detail which factors control the usage of one chaperone system over another. We find that the different chaperone systems do not operate orthogonally and can compensate for each other when one system is disabled or overworked, and that this can complicate the analysis of "knockout" experiments, where the concentration of native protein is compared both with and without the presence of a given chaperone system. This study also gives a general recipe for conducting a transition-path-based analysis on a network of coupled chemical reactions, which can be useful in other types of networks as well.

The size of each node is proportional to the logarithm of its concentration after running the FoldEco model with a given set of parameters (the “Default” protein, at , and a synthesis rate of , see Section “Four characteristic protein profiles” for more information). The nodes are colored to highlight the different chaperone systems in the network. Colons placed between two, three or four species denote complexes, and the special notation “GrLd:{X,Y}:GrS” denotes a protein in the X state bound in the cis ring of the GroEL/GroES complex, and a second protein in the Y state bound in the trans ring. As these states are separated into two, depending on whether we are tracking the X, or the Y protein (see Section “Extracting a rate matrix”), we denote the resulting two states as GrLd:{X,y}:GrS and GrLd:{x,Y}:GrS, with the capitol letter marking which protein molecule we are tracking. For simplicity, aggregates of all sizes are denoted here by A, although in practice each aggregate size from to here is given a unique state. There are reversible transitions between aggregates of size and size , which are not shown here. denotes an aggregate that has been prepared for ClpB binding, and denotes that the protein is now committed to degradation.

The relative pathway probabilities are studied as a function of synthesis rate for the four characteristic proteins examined here. “dir” labels the direct flux, and “deg” labels the flux occurring by degradation followed by resynthesis. The biophysical profiles for the four proteins are given in .

Comparison of the ratios of populations of the KJE and B+KJE pathways from M to U with the concentrations in the misfolded and aggregate states.

The points are computed from all proteins at all synthesis rates for which the concentration in the aggregate state (and hence the population of the B+KJE pathway) is greater than zero. The solid line is the best fit to the function , with , where , and is the ratio of the concentration of misfolded and aggregated protein.

(a) Comparison of transition rates from the misfolded state into the state (in the KJE system) and the state (in the GroELS system), for all four model proteins. (b) Comparison of committor probabilities from the and states to the unfolded state. In other words, these are the probabilities that, starting from either or , the unfolded state will be reached before the misfolded state.

(a) The concentration at of the native, unfolded, misfolded and total aggregated species both with and without the GroELS system for the Default protein at a ribosome activation rate of . Although the network with GroELS knocked out has higher concentrations of unfolded and misfolded protein, it keeps approximately the same native state concentration. (b) Pathway flux from the misfolded to the unfolded state through the three chaperone systems both with and without the GroELS system. We see that the absence of GroELS is more than made up for by enhanced usage of the B+KJE system.

A multiplicative factor is used to simultaneously modify GroEL and DnaK binding rates for unfolded and misfolded protein. The GroEL-binding rates used here are multiplied by , and the DnaK-binding rates are divided by . (a) The Default protein at low synthesis rate prefers the KJE pathway at , but this preference is shifted to favor the GroELS pathway at high values. (b) The Slow Folder protein at low synthesis rate prefers the GroELS pathway at , and this preference is only partially shifted to favor the KJE pathway at low values. (c) Although the transition rate into the KJE pathway increases with decreasing , the committor probability (the probability of reaching the unfolded state before returning to the misfolded state) decreases, causing the nonmonotonic behavior in (b).

(a–d) The pathway flux through GroELS (solid bars) is shown as well as the direct folding flux (transparent bars), for different concentrations of GroEL chaperone. The concentration of total GroEL is varied by a multiplicative factor ranging from to . , the reference value of GroEL chaperone, is equal to , which is the value used in Section “Correcting misfolded states”. The concentration of GroES is varied along with GroEL by the same multiplicative factor, where equals . Panels (a–d) show data for the Default, Slow Folder, Bad Folder and Aggregator proteins respectively, with the colors corresponding to the legend of panel (f) (e) The concentration of unfolded protein at the evaluation time (). Colors for each protein correspond to those used in the above panels, and also to the legend in panel (f). (f) Concentration of the native state for each protein. Since the Default, Slow Folder and Bad Folder proteins do not strongly depend on the GroELS system, we call them “class-I/II substrates” according to the nomenclature of Kerner et al. . In contrast, the concentration of the native state for the Aggregator protein strongly depends on the concentration of total GroEL, indicating that it should be called a “class-III” substrate.